Cryptography, Information Theory, and Error-Correction. Aiden A. Bruen

under the supervision of M. Epstein. Dr. Forcinito is the CTO of AP Dynamics, an engineering company in Calgary. He currently holds an Adjunct Professor position at the Schulich School of Engineering, University of Calgary and is an industrial engineering consultant in the energy area in Calgary.

      James M. McQuillan grew up in Ottawa, Canada. He obtained his Undergraduate and Master's degrees from Carleton University in Ottawa and the University of Vermont and his doctorate from the University of Western Ontario (now Western University) in London, Canada. Dr. McQuillan is a Professor in the School of Computer Sciences at Western Illinois University.

Part I Mainly Cryptography

Chapter 1 Historical Introduction and the Life and Work of Claude E. Shannon

      Goals, Discussion We present here an overview of historical aspects of classical cipher systems. Our objective is to give the reader a panoramic view of how the fundamental ideas and important developments fit together. This overview does not pretend to be exhaustive but gives a rough time line of development of the milestones leading to modern cryptographic techniques. The reader interested in a complete historical review is advised to consult the definitive treatise by Kahn [Kah67].

1.1 Historical Background

      Cryptology is made up of two Greek words kryptos, meaning “hidden,” and lógos meaning “word.” It is defined [Bri19] as the science concerned with data communication and storage in secure and usually secret form. It encompasses both cryptography (from the Greek graphia meaning writing) and cryptanalysis or the art of extracting the meaning of a cryptogram.

Cryptography has a history that is almost as long as the history of the written word. Some four millennia ago (see [Kah67, p. 71]), an Egyptian scribe recorded in stone the first known hieroglyphic symbol substitution in the tomb of Khnumhotep II, a nobleman of the time. Although the intention in this case was to exalt the virtues of the person, rather than to send a secret message, the scribe used for the first time one of the fundamental elements used by cryptographers throughout the ages, namely substitution. He used unusual hieroglyphic symbols, known perhaps only to the elite, in place of the more common ones.

      In substitution, the sender replaces each letter of a word in a message by a new letter (or sequence of letters or symbols) before sending the message. The recipient, knowing the formula used for the substitution – the secret key – is able to reconstruct the message from the scrambled text that was received. It is assumed that only the recipient and the sender know the secret key.

      The other main cryptographic technique used is transposition (or permutation) in which the letters of the message are simply rearranged according to some prescribed formula which would be the secret key in that case.

      The Greeks were the inventors of the first transposition cipher. The Spartans [Kah67] in the fifth century BCE, were the first recorded users of cryptography for correspondence. They used a secret device called a scytale consisting of a tapered baton around which was spirally wrapped either a strip of parchment or leather on which the message was written. When unwrapped, the letters were scrambled, and only when the strip was wrapped around an identically sized rod could the message be read.

      Today, even with the advent of high‐speed computers, substitution and transposition form the fundamental building blocks of ciphers used in symmetric cryptography.

To put it in a historical perspective, asymmetric or public key cryptography was not invented until the 1970s. Exactly when it was invented, or who should take most of the credit, is an issue still in dispute. Both the NSA¹ and the CESG² have claimed priority in the invention of public key cryptography.

      Cryptography has had several reincarnations in almost all cultures. Because of the necessity of keeping certain messages secret (i.e. totally unknown to potential enemies) governments, armies, ecclesiastics, and economic powers of all kinds have been associated throughout history with the development of cryptography. This trend continues today.

The Roman General Julius Caesar was the first attested user of substitution ciphers for military purposes [Kah67, p. 83]. Caesar himself recounted this incident in his Gallic Wars. Caesar found out that Cicero's station was besieged and realized that without help, he would not be able to hold out for long. Caesar had a volunteer ride ahead, with an encrypted message fastened to a spear which he hurled into the entrenchment. Basically, Cicero was told to keep up his courage and that Caesar and his legions were on their way.

      In the cipher form used by Caesar, the first letter of the alphabet “A” was replaced by the fourth letter “D,” the second letter “B” by the fifth “E,” and so on. In other words, each original letter was replaced by one three steps further along in the alphabet. To this day, any cipher alphabet that consists of a standard sequence like Caesar's is called a Caesar alphabet even if the shift is different from three.

      Not much mention is made of the coding abilities of Augustus Caesar, the first Emperor of Rome and nephew of Julius Caesar. His cipher involved a shift of only one letter so that for the plain text (that is the original text) A was enciphered as B.

      Mention of cryptography abounds in early literature: Homer's Iliad refers to secret writing. The Kama‐sutra, the famous text book of erotics from the Indian subcontinent, lists secret writing as one of the 64 arts or yogas that women should know and practice [Kah67, p. 75]. One of the earliest descriptions of the substitution technique of encryption is given therein. One form involves the replacement of vowels by consonants and vice versa.

      In Hebrew literature, there are also examples of letter substitution. The most prevalent is the atbash technique. Here the first and last, second and second last, and so on, letters of the Hebrew alphabet are interchanged. An example can be found in the Old Testament of the Bible. Kahn [Kah67, p. 77] cites Jeremiah 25: 26 and Jeremiah 51: 41, where the form “SHESHACH appears in place of Babel (Babylon).”

      In Jeremiah 51: 41, the phrase with SHESHACH is immediately followed by one using “Babylon.” To quote:

      How is SHESHACH taken!

      And the praise of the whole earth seized!

      How is Babylon become an astonishment

      Among the nations!

      Through Aramaic paraphrases of the Bible, it is clear that SHESHACH is the same as Babel. With the atbash technique, the second letter of the Hebrew alphabet “b” or beth becomes the repeated SH or SHIN, the next to last letter in the alphabet. Similarly, the “l” of lamed, becomes the hard ch, or kaph of SHESHACH. Since Babylon appears below, the use of atbash here was not to actually hide the word but perhaps just a way for the scribe to leave a trace of himself in the work he was copying.

The first people to clearly understand the principles of cryptography and to elucidate the beginnings of cryptanalysis were the Arabs [Kah67]. While Europe was in the Dark Ages, Arab arts and science flourished and scholars studied methods of cryptanalysis, the art of unscrambling secret messages without knowledge of the secret key. A complete description of this work, however, was not published until the appearance of the multivolume Subh al‐a'sha by about 1412.

      European cryptology was being developed around this time in the Papal States and the Italian city‐states [Kah67]. The first European manual on cryptography (c1379) was a compilation of ciphers by Gabriele de Lavinde of Parma, who served Pope Clement VII. The Office of Cipher Secretary to the Pope was created in 1555. The first incumbent was Triphon Bencio de Assisi. But considerably before this in 1474, Cicco Simonetta wrote a manuscript that was entirely devoted to